I cannot stress this enough: Nils is right, NFC is not really a technology where the term "radio wave propagation" applies; RFID in general isn't.
The point is that in real antennas, you generate a wave front that propagates through space, until it hits the receiver. For NFC, that is not the case.
Here, you essentially build a transformer with the primary coil being the reader and the secondary coil being the NFC tag. Through the amount of power the tag takes out of the magnetic field, data is exchanged. This is fundamentally different from antennas, and power goes down with \$d^3\$, instead of \$d^2\$ as with wave propagation (and antennas of a finite effective area), \$d\$ being the distance between transmitter and receiver.
So, no, without a big, powerful system you cannot extend the range of NFC, as dictated by physics.
Now, you say "carry in a bag": This can work, because the NFC coil in e.g. a smart phone is really small, and a bag can get pretty large. The question really is how far this will work. Assuming your original NFC range was 4cm, and you want to get e.g. to 40cm = 4cm * 10, your transmitter would need to be \$10^3\$ times as powerful and sensitive to allow for the necessary energy to inductively "couple over" from reader coil to tag coil.
Still, communication probably wouldn't work – the further you get from the coil, the less "reaction" you can measure when someone extracts energy from your field (hence the increase in necessary sensitivity). If you can build a device with \$10^3 \cdot 10^3\$ the dynamic range of commercial NFC readers, you'd definitely reached a level that would exceed "school project" ambitions and count as "serious commercial or academic research done by people with years of experience". Also, at some point, the energy that doesn't couple into the tag, but is lost due to being radiated as wave (involuntarily) or coupled into other conductive materials will be considered harmful interference.